1. Field of the Invention
This invention relates to holography and, more particularly, to holographic transparencies that control both amplitude and phase transmittance.
2. Description of the Prior Art
In general, a hologram is a photographic recording of the interference pattern formed by an object wave and a reference wave. The object wave is usually a complex wave created by reflecting a beam of coherent light off of the object being recorded. The reference wave is usually a beam of coherent light coming directly from the same source. The object wave and the reference wave are combined together to generate an interference pattern that is recorded on a photographic transparency, called a hologram. To reconstruct an image of the original object, the hologram is illuminated with a reconstructing beam of light having the same characteristics as the phase coherent, reference wave used in forming the hologram.
The term "reconstruct the image" as used throughout the specification and claims of this case means that the hologram is illuminated and an image appears and includes the formation of an image of an object that does not physically exist and also includes the modulation of an incident wave in an arbitrary but controlled manner, without necessarily forming a specific image.
Holograms can also be synthesized by using a digital computer, and the object being recorded on the hologram need not physically exist. A mathematical model of the object is usually made in the form of a matrix array of phase coherent point sources. Next, the wave front mathematically produced by the object and incident on a plane in space, called the hologram plane, is calculated. The results of the calculation are optically displayed and the complex pattern thus generated is photographically recorded on a photosensitive film. When illuminated by a reconstructing beam in the conventional manner, the photosensitive film will modulate the wave so that the wave front will emerge from the hologram exactly as though it came from the object.
Heretofore, the major problem in making computer synthesized holograms was forming a transparency that could control both the amplitude and the phase of a reconstructing wave at each point on the surface of the hologram. One solution to this problem has been to make a transparency that controls just the amplitude transmittance of the reconstructing light and a separate transparency that controls just the phase of the reconstructing light. Thereafter, the two transparencies are mounted together to form a sandwich. Unfortunately, however, the alignment between the two transparencies is so critical that so far only crude patterns have been able to be encoded and holographically reconstructed.
Another well known technique for controlling the amplitude and phase of a computer generated hologram is known as the detour-phase binary hologram. In this technique the hologram is divided into a plurality of small cells each representing a complex Fourier coefficient. Each cell contains an aperture with its area related to the amplitude transmittance and its position with respect to the boundaries of the cell related to the phase of the Fourier coefficient. When a plurality of these cells is illuminated, the desired image is obtained off-axis in the first defraction order.
Although the detour-phase binary hologram requires only one transparency to control both amplitude and phase transmittance, the ultimate complexity of this type of hologram is limited in terms of its maximum space-bandwidth product. In order to minimize the amplitude and the phase quantization error, each Fourier coefficient, or cell, must be encoded into a large number of subcells. Each subcell on the transparency is exposed individually by illumination from a separate display resolution element located in an optical display device such as a cathode-ray tube. Since all of the display devices have only a finite number of display resolution elements available, the ultimate complexity of the hologram in terms of the maximum number of Fourier coefficients encodable is limited by the physical characteristics of the optical display device.
A further problem with binary detour-phase holograms is the quantization noise originating from quantizing the amplitude and phase valves in each cell on the hologram. An additional limitation of the binary detour-phase hologram is the limited lighting efficiency obtainable for the image. Since the desired image appears in but one of a plurality of diffraction orders, the light diffracted to the image is only a small fraction of the total illumination incident on the hologram. Moreover, a further problem with binary detour-phase holograms is the limitation of the maximum size of an object that can be spatially filtered. Since the binary detour-phase hologram generates spurious images, these images will overlap onto the desired image when an object is reconstructed that is too large for the system.
Another well known optical transparency for reconstructing light beams is called a kinoform. The kinoform is an optical transparency in which the amplitude data is approximated by a constant factor and only the phase data is recorded on the transparency. The Fourier transformed amplitude data is discarded on the assumption that only the phase information contained in the wave front scattered from an object is required for a faithful image of the scattering object. Since the amplitude information about the wave front is not preserved, a kinoform is not technically a hologram. A further description of a kinoform technique can be found in U.S. Pat. No. 3,606,515, entitled "Method of Manufacturing Wave Shaping Objects":, issued Messrs. Hirsch, Jordan, and Lesem on Sept. 20, 1971.